The 20+B+b is not really double counting. As an
extreme example to check this, assume q=1, B=30, and
b=30, and you're on the first question of the match. If
you waited until the end of the question, the score
would be 40 to 0 (you're up by 40). If you neg, the
score is -5 to 40 (you're down by 45). The neg then,
cost you 85 points, -5+q(B+b+20), not q(-5-10-b),
which would be 45.